In the present work, we intentionally focus on simple single segmentation fields on \(3D\)  meshes and the clustering is obtained applying
a well know clustering algorithm, k-means++, in order to achieve straightforwardly a fair comparison of our segmentation method with the spectral method. Nevertheless, our farthest point based segmentation FSS method may be extended to more complicated scenarios, where several attributes are combined in a single segmentation field, such as in [1]}, [2]} or where several multi-view clustering methods have been proposed to integrate without supervision multiple information from the data, [3]}, [4]}. Therefore, in the future, we plan to investigate the advantages of replacing Nyström's method with ours, for instance, compare with [5]}, [6]}, in order to make the proposed algorithms more efficient in terms of computational and memory complexity as well as to obtain segmentations without artifacts, such as nonconnected clusters. Finally, it is worth mentioning that the basic ideas of our segmentation method - to compute only few columns of the affinity matrix and to apply a clustering algorithm to the rows of this submatrix - could be straightforwardly used in other segmentation or clustering problems, for instance in segmentation of digital images [7]}.
